[rfugger]

Unfortunately, restricting to only computable maths means disallowing the natural numbers, basic arithmetic, or any equivalent structure, since Gödel incompleteness would apply. I doubt any system without access to the full set of natural numbers or basic arithmetic could qualify as "general AI".

[asdfasgasdgasdg]

Pardon my ignorance. Computers appear to be able to perform basic arithmetic. For example, you can open up the console in your browser and find that the sum of two and two is indeed four. So it is not entirely obvious to me how basic arithmetic is non-computable.

[krastanov]

If you permit infinitely many integers it becomes problematic. If you are dealing with a finite entity (e.g. the finite part of the universe that can affect us), then there are no problems.

[Udik]

Can you sum correctly two arbitrarily large integers?

[asdfasgasdgasdg]

I don't think it matters, right? Since arbitrarily large integers are not things that occur in the physical world.

[YeGoblynQueenne]

How do you know all those things about the physical world? For example- you say that "all of the physical laws of the universe are defined by computable maths". Do you really know what all the physical laws of the univese are?

[asdfasgasdgasdg]

We don't know. We just think it likely. We are unaware of counterexamples, or reasons to suspect the existence of counterexamples.

[rfugger]

Gödel incompleteness applies to any system capable of basic arithmetic.

[asdfasgasdgasdg]

I'm unsure how this matters? The physical universe does not prove itself and does not need to. Godel's theorems just say that certain types of mathematical systems can't prove themselves, which seems quite irrelevant to simulating the universe. Please explain if I'm missing something.